Return a random vector from the \(\ndim\)-dimensional MultiVariate Uniform Parallelepiped (MVUP) Distribution.
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Detailed Description

Return a random vector from the \(\ndim\)-dimensional MultiVariate Uniform Parallelepiped (MVUP) Distribution.

See the documentation of pm_distUnifPar for details of the definition of the PDF.

Parameters

[in,out]	rand	: The input/output vector of shape `(1:ndim)` of, type `real` of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128). On input, it must contain a vector of randomly uniformly-distributed numbers in the range \([0, 1)\). On output, it will contain a random vector from the support of the target distribution.
[in]	lb	: The input scalar or `contiguous` vector of the same type and kind as the output argument `rand`. If `ub` is a scalar, then `lb` must be a scalar representing the lower bound of the `ndim`-dimensional hyper-cube support of the distribution. If `ub` is a vector, then `lb` must be a vector representing the lower bound of the `ndim`-dimensional hyper-rectangle support of the distribution. If `ub` is a matrix, then `lb` must be a vector representing the origin of the coordinate system with respect to which the `ndim`-dimensional hyper-parallelepiped support of the distribution is determined. (optional. default = `0`)
[in]	ub	: The input scalar or `contiguous` vector/matrix of the same type and kind as the output argument `rand`. If `ub` is a scalar, it must contain the upper bound of the `ndim`-dimensional hyper-cube support of the distribution. In such a case, the input optional argument `ndim` must be specified. If `ub` is a vector of shape `(1:ndim)`, it must contain the upper bounds of the `ndim`-dimensional hyper-rectangle support of the distribution along each dimension. If `ub` is a square matrix of shape `(1:ndim, 1:ndim)`, it must contain the representative matrix of the `ndim`-dimensional hyper-parallelepiped support of the distribution.

Possible calling interfaces ⛓

: use pm_distUnifPar, only: setUnifParRand

call random_number(rand(1:ndim))

call setUnifParRand(rand(1:ndim), ub) ! Uniform Hyper-cube support starting at the origin.

call random_number(rand(1:ndim))

call setUnifParRand(rand(1:ndim), lb, ub) ! Uniform Hyper-cube support with lower bound `lb`.

call random_number(rand(1:ndim))

call setUnifParRand(rand(1:ndim), ub(1:ndim)) ! Uniform Hyper-rectangle support starting at the origin.

call random_number(rand(1:ndim))

call setUnifParRand(rand(1:ndim), lb(1:ndim), ub(1:ndim)) ! Uniform Hyper-rectangle support with lower bound `lb`.

call random_number(rand(1:ndim))

call setUnifParRand(rand(1:ndim), ub(1:ndim, 1:ndim)) ! Uniform Hyper-parallelepiped support starting at the origin.

call random_number(rand(1:ndim))

call setUnifParRand(rand(1:ndim), lb(1:ndim), ub(1:ndim, 1:ndim)) ! Uniform Hyper-parallelepiped support starting at `lb`.

!

pm_distUnifPar::setUnifParRand
Return a random vector from the -dimensional MultiVariate Uniform Parallelepiped (MVUP) Distribution.
Definition: pm_distUnifPar.F90:920

pm_distUnifPar
This module contains classes and procedures for setting up and computing the properties of the MultiV...
Definition: pm_distUnifPar.F90:92

Warning: The condition all(0. <= rand .and. rand < 1.) must hold for the corresponding input arguments.
The condition all(size(rand) == size(lb(:))) must hold for the corresponding input arguments.
The condition all(size(rand) == shape(ub)) must hold for the corresponding input arguments.
The condition all(lb /= ub(:)) must hold for the corresponding input arguments.
Although there is theoretically no limit on the possible values of lb and ub with respect to each other, the condition all(lb(:) < ub(:)) is expected (but not checked) to hold for the corresponding input arguments.
The input representative matrix of the parallelepiped support of the distribution ub(:,:) must be non-singular.
In other words, the columns of the matrix must span the \(\mathbb{R}^{\ndim}\) space.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.; The pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds.

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK, LK

4 use pm_io, only: display_type

5 use pm_distUnifPar, only: setUnifParRand

6

7 implicit none

8

9 real :: rand(5)

10

11 type(display_type) :: disp

12 disp = display_type(file = "main.out.F90")

13

14 call disp%skip()

15 call disp%show("call random_number(rand(1:2))")

16 call random_number(rand(1:2))

17 call disp%show("call setUnifParRand(rand(1:2), ub = 1.)")

18 call setUnifParRand(rand(1:2), ub = 1.)

19 call disp%show("rand(1:2)")

20 call disp%show( rand(1:2) )

21 call disp%skip()

22

23 call disp%skip()

24 call disp%show("call random_number(rand(1:2))")

25 call random_number(rand(1:2))

26 call disp%show("call setUnifParRand(rand(1:2), lb = -100., ub = 1.)")

27 call setUnifParRand(rand(1:2), lb = -100., ub = 1.)

28 call disp%show("rand(1:2)")

29 call disp%show( rand(1:2) )

30 call disp%skip()

31

32 call disp%skip()

33 call disp%show("call random_number(rand(1:5))")

34 call random_number(rand(1:5))

35 call disp%show("call setUnifParRand(rand(1:5), ub = [1., 2., 3., 4., 5.]) ! random vector of dimension 5.")

36 call setUnifParRand(rand(1:5), ub = [1., 2., 3., 4., 5.])

37 call disp%show("rand(1:5)")

38 call disp%show( rand(1:5) )

39 call disp%skip()

40

41 call disp%skip()

42 call disp%show("call random_number(rand(1:5))")

43 call random_number(rand(1:5))

44 call disp%show("call setUnifParRand(rand(1:5), lb = -[1., 2., 3., 4., 5.], ub = [1., 2., 3., 4., 5.]) ! random vector of dimension 5.")

45 call setUnifParRand(rand(1:5), lb = -[1., 2., 3., 4., 5.], ub = [1., 2., 3., 4., 5.])

46 call disp%show("rand(1:5)")

47 call disp%show( rand(1:5) )

48 call disp%skip()

49

50 call disp%skip()

51 call disp%show("call random_number(rand(1:2))")

52 call random_number(rand(1:2))

53 call disp%show("call setUnifParRand(rand(1:2), ub = reshape([1., 1., -1., -1.], shape = [2, 2]))")

54 call setUnifParRand(rand(1:2), ub = reshape([1., 1., -1., -1.], shape = [2, 2]))

55 call disp%show("rand(1:2)")

56 call disp%show( rand(1:2) )

57 call disp%skip()

58

59 call disp%skip()

60 call disp%show("call random_number(rand(1:2))")

61 call random_number(rand(1:2))

62 call disp%show("call setUnifParRand(rand(1:2), lb = [10., 10.], ub = reshape([1., 1., -1., -1.], shape = [2, 2]))")

63 call setUnifParRand(rand(1:2), lb = [10., 10.], ub = reshape([1., 1., -1., -1.], shape = [2, 2]))

64 call disp%show("rand(1:2)")

65 call disp%show( rand(1:2) )

66 call disp%skip()

67

68 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

69 ! Output an example array for visualization.

70 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

71

72 block

73 use pm_arraySpace, only: setLinSpace

74 real :: rand(2, 4)

75 integer(IK) :: fileUnit, i

76 open(newunit = fileUnit, file = "setUnifParRand.RK.txt")

77 do i = 1, 1000

78 call random_number(rand)

79 call setUnifParRand(rand(:,1), lb = -[2., 2.], ub = -[0., 1.])

80 call setUnifParRand(rand(:,2), ub = reshape([1., 1., -1., +1.], shape = [2, 2]))

81 call setUnifParRand(rand(:,3), lb = [2.0, -2.], ub = reshape([1., 1., +2., -2.], shape = [2, 2]))

82 call setUnifParRand(rand(:,4), lb = [1.5, -.5], ub = reshape([2., 1., 1., 2.], shape = [2, 2]))

83 write(fileUnit, "(*(g0,:,','))") rand

84 end do

85 close(fileUnit)

86 end block

87

88end program example

pm_arraySpace::setLinSpace
Return the linSpace output argument with size(linSpace) elements of evenly-spaced values over the int...
Definition: pm_arraySpace.F90:324

pm_io::show
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726

pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508

pm_arraySpace
This module contains procedures and generic interfaces for generating arrays with linear or logarithm...
Definition: pm_arraySpace.F90:33

pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252

pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393

pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268

pm_kind::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541

pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540

pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539

pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe

2set PATH=..\..\..\lib;%PATH%

3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe

4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example output ⛓
1

2call random_number(rand(1:2))

3call setUnifParRand(rand(1:2), ub = 1.)

4rand(1:2)

5+0.781265080, +0.532456040E-1

6

7

8call random_number(rand(1:2))

9call setUnifParRand(rand(1:2), lb = -100., ub = 1.)

10rand(1:2)

11-10.3243999, -74.8121109

12

13

14call random_number(rand(1:5))

15call setUnifParRand(rand(1:5), ub = [1., 2., 3., 4., 5.]) ! random vector of dimension 5.

16rand(1:5)

17+0.494812012, +1.52667940, +0.769848168, +0.321944237, +0.520732701

18

19

20call random_number(rand(1:5))

21call setUnifParRand(rand(1:5), lb = -[1., 2., 3., 4., 5.], ub = [1., 2., 3., 4., 5.]) ! random vector of dimension 5.

22rand(1:5)

23-0.861980915, -1.60144782, -1.70312214, -3.72094870, +3.03106236

24

25

26call random_number(rand(1:2))

27call setUnifParRand(rand(1:2), ub = reshape([1., 1., -1., -1.], shape = [2, 2]))

28rand(1:2)

29-0.135914207, -0.135914207

30

31

32call random_number(rand(1:2))

33call setUnifParRand(rand(1:2), lb = [10., 10.], ub = reshape([1., 1., -1., -1.], shape = [2, 2]))

34rand(1:2)

35+10.7439728, +10.7439728

36

37

Postprocessing of the example output ⛓
1#!/usr/bin/env python

2

3import matplotlib.pyplot as plt

4import pandas as pd

5import numpy as np

6import glob

7import sys

8

9linewidth = 2

10fontsize = 17

11

12for kind in ["RK"]:

13

14 pattern = "*." + kind + ".txt"

15 fileList = glob.glob(pattern)

16

17 for file in fileList:

18

19 df = pd.read_csv(file, delimiter = ",", header = None)

20

21 # definitions for the axes

22 #left, width = 0.1, 0.65

23 #bottom, height = 0.1, 0.65

24 #spacing = 0.015

25

26 # start with a square Figure

27 fig = plt.figure(figsize = (8, 6))

28

29 plt.rcParams.update({'font.size': fontsize - 2})

30 ax = plt.subplot()

31 #ax = fig.add_axes([left, bottom, width, height]) # scatter plot

32 #ax_histx = fig.add_axes([left, bottom + height + spacing, width, 0.2], sharex = ax) # histx

33 #ax_histy = fig.add_axes([left + width + spacing, bottom, 0.2, height], sharey = ax) # histy

34 #

35 #for axes in [ax, ax_histx, ax_histy]:

36 # axes.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")

37 # axes.tick_params(axis = "y", which = "minor")

38 # axes.tick_params(axis = "x", which = "minor")

39 #

40

43

44 # the scatter plot:

45 for i in range(0, len(df.values[0,:]), 2):

46 ax.scatter ( df.values[:,i]

47 , df.values[:,i+1]

48 , s = 8

49 , zorder = 1000

50 )

51

52 #ax_histx.hist(df.values[:, 0], bins = 50, zorder = 1000)

53 #ax_histy.hist(df.values[:, 1], bins = 50, orientation = "horizontal", zorder = 1000)

54

55 ax.set_aspect("equal")

56 ax.set_xlabel("X", fontsize = 17)

57 ax.set_ylabel("Y", fontsize = 17)

58 plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")

59 plt.minorticks_on()

60

61 plt.tight_layout()

62 plt.savefig(file.replace(".txt",".png"))

Visualization of the example output ⛓

Test:: test_pm_distUnifPar

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Amir Shahmoradi, April 23, 2017, 12:36 AM, Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin

Definition at line 920 of file pm_distUnifPar.F90.

The documentation for this interface was generated from the following file:

src/fortran/main/pm_distUnifPar.F90